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Abstract <p> The first boundary value problems (internal and external) for a two-dimensional filtrationflow of a liquid in a non-uniform porous layer of variable thickness and permeability are studied.The given discrete sources of the flow are located in the flow region and are modeled bysingularities (isolated singular points) of the complex potential. The boundary of the flow region ismodeled by an arbitrary smooth (piecewise smooth) closed contour. The pressure distribution onthe boundary is characterized by a given function that has discontinuities of the first kind.A method for regularizing (smoothing) the boundary condition is proposed, which allows reducingthe problems to a boundary singular integral equation with a weak singularity and with smoothright-hand side. This regularization method is applied to the solution of a boundary valueproblem modeling the operation of a system of wells in a heterogeneous soil layer (formation) onwhose supply contour the given pressure distribution (the generalized potential) experiencesdiscontinuities of the first kind.</p>

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Boundary Value Problem of Two-Dimensional Filtration of a Liquid in an Inhomogeneous Layer with a Boundary Condition Having Discontinuity of the First Kind

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • V. F. Piven’

摘要

Abstract

The first boundary value problems (internal and external) for a two-dimensional filtrationflow of a liquid in a non-uniform porous layer of variable thickness and permeability are studied.The given discrete sources of the flow are located in the flow region and are modeled bysingularities (isolated singular points) of the complex potential. The boundary of the flow region ismodeled by an arbitrary smooth (piecewise smooth) closed contour. The pressure distribution onthe boundary is characterized by a given function that has discontinuities of the first kind.A method for regularizing (smoothing) the boundary condition is proposed, which allows reducingthe problems to a boundary singular integral equation with a weak singularity and with smoothright-hand side. This regularization method is applied to the solution of a boundary valueproblem modeling the operation of a system of wells in a heterogeneous soil layer (formation) onwhose supply contour the given pressure distribution (the generalized potential) experiencesdiscontinuities of the first kind.